ON GEAPHIC METHODS IN MECHANICAL SCIENCE. 



381 



] or, if Cartesian co-ordinates are used, the heights of the tide as ordinates, 

 and corresponding times measured from a certain hour, say noon, as 

 abscissEe. Such an actual diagram is given (fig. 9). 



This at once represents two facts, which have an intimate connection, 

 and we can see the great advantage of the two-dimension system, for now 

 we compare graphically the effect of change of time on the height of the 

 tide — that is to say, not merely the relation of the various heights to each 

 other, but their relative value as affected by lapse of time. 



This is, however, but one of the two advantages : the other is that. 



Fig. 10. 



Hoitr.sAJf Hours SJif. 



iP-NIGHT 7 Z 3 I: 6 6 7 a 9 W //NOON / Z 3 •» v5 <»' 7 _S 3 70 I) MIO-NIQHT 



illDNlGHT J Z <S 



7 S O /O 7/ NOON / X JJ -i', .5 



^ 70 77 MIO NIGHT 



having no longer to notify each value of the height by some symbol to 

 show what hour of the tide it corresponds to, thus necessarily limiting 

 the number of heights which could conveniently be given, each point 

 representing height now has its particular time given by its abscissa. 

 Hence an unlimited number of heights can be given, since an unlimited 

 number of points can be shown. As a matter of fact, the tide, rising 

 and falling with the lapse of time, necessarily has an infinite number of 

 heights, and the points representing these merge into the continuous line 

 given in fig. 9. 



